Homework Help: Knowing the Energy of a photon, what is the charge of a species?

1. Nov 4, 2017

brbrett

1. The problem statement, all variables and given/known data
An atom or ion with only one electron is excited from the ground state to the first excited state (n = 2) with a photon of 1.47E-17 J of energy. What is the charge on the one-electron species?
A. 0
B. +1
C. +2
D. +3
E. +4

2. Relevant equations
E=-(2.18E-18)(Z2)/(N2)

3. The attempt at a solution
I plugged in the information given into the equation:

(1.47E-17)=(-2.18E-18)(Z2)((1/4)-1)

With some algebra, I got Z=2.998, which may as well be a charge of +3.
However, according to the answer key, the correct answer is, in fact, +2 (C).
I would appreciate any guidance as to where I might be going wrong with this problem. :)

2. Nov 4, 2017

Orodruin

Staff Emeritus
What is the charge of the ion as a whole if the charge of the nucleus is 3?

3. Nov 4, 2017

brbrett

Due to shielding, the effective charge would be about +2? I think I kinda see that maybe my calculations weren't wrong, but that I didn't understand the question right, but I still don't really get it.

4. Nov 4, 2017

Staff: Mentor

You calculated Z, but Z is not what the question asks about. It asks you to calculate charge of the ion, not of the nucleus.

5. Nov 4, 2017

brbrett

Ah, so then because I calculated the nucleus' charge to be +3, with a single electron there would be a charge of +2? That would make a lot of sense. Then I assume I didn't make any mistakes in solving for charge of the nucleus to figure out the ion's charge? Thanks!

6. Nov 5, 2017

Staff: Mentor

Looks OK, although your first equation and the second equation are different.

7. Nov 5, 2017

Thanks!